"Establish Justice"
As the Constitution states "We the People of the United States, in Order to form a more perfect Union, establish Justice, (...)"
The Court System is established in Article III as part of the Judicial branch of the U.S. government; its main goal is to establish justice by interpreting and evaluating the laws and ensuring that none of the other branches of the government (executive and legislative) abuses of their powers by determining if their acts are constitutional or not (Judicial Review).